Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane

Details Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane

2009-10-12

arxiv.org/abs/0910.2151v2

Mod. Phys. Lett. A 25 (2010) 15-24

Physics

Mathematical Physics

12 pages, no figure; minor changes; published version

Scientific paper

The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians $H_k$, $k=1$, 2, 3,..., on a plane. The elements of the dihedral group $D_{2k}$ are realized as operators on this plane and used to define some differential-difference operators $D_r$ and $D_{\varphi}$. The latter serve to construct $D_{2k}$-extended and invariant Hamiltonians $\chh_k$, from which the starting Hamiltonians $H_k$ can be retrieved by projection in the $D_{2k}$ identity representation space.

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